When I try to launch any game from steam the popup with "Launching game" appears and steam says "running" but the game doesn't start. I tried both native version and proton. For native games I am able to run them if I launch them directly from the executable.
From what I can tell from the Steam output, it looks like its trying to run Proton GE that is missing files. I am guessing it was a older forced setting before Proton GE updated to GE-2.
Try force running Brawlhalla in Proton 6.3-7 if you haven't already.
Something else to keep in mind is that Proton GE 6.15 introduced changes to the prefix directory structure - older prefixes won't work without manual intervention.